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Power series for integral (1/x) dx

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data
    I have to find the power series representation for integral (1/x) dx


    2. Relevant equations

    ln (1+x)

    3. The attempt at a solution
    This is very similar to ln(1+x) but I don't know if this helps me.

    Is this ln(x) shifted one to the right? So maybe I can use what is already the power series for ln(1+x) = Ʃ (-1)^(n-1) (x^n)/n from n = 1 to ∞

    so could I do ln(x) = [(-1)^(n) (x^(n+1)] / (n+1)

    NO? Maybe I shifted it wrong?
     
  2. jcsd
  3. Dec 4, 2013 #2

    Mark44

    Staff: Mentor

    ##\int \frac{dx}{x} = ln(x) + C##, assuming x > 0.

    ln(x + 1) is the translation by one unit left, not right, of the graph of y = ln(x).
     
  4. Dec 5, 2013 #3
    OK so this

    Ʃ (-1)^(n-1) (x^n)/n from n = 1 to ∞

    Should be Ʃ (-1)^(n-2) (x^(n-1))/(n-1) from n = 1 to ∞

    Right?
     
  5. Dec 5, 2013 #4

    Mark44

    Staff: Mentor

    Instead of writing "answers" show me some mathematics reasoning.
     
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